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That elegant sinusoidal waviness rippling through a high-altitude contrail is not turbulence, and it is not wind. It is a fluid dynamic instability with a name: the Crow instability, first characterised by S. C. Crow in 1970. Every finite wing generating lift sheds two counter-rotating vortices from its tips. The pressure differential that keeps the aircraft aloft spills around each tip and rolls up into a concentrated trailing pair, separated by roughly (pi/4) of the wingspan for elliptical loading. Left alone, these vortices would descend together, serene, under their mutual induction. They are not left alone. Each vortex sits inside the velocity field of its partner, and any faint perturbation along its length gets amplified by the strain that field imposes. The outcome is a slow, symmetric, long-wavelength oscillation: - The most amplified wavelength is around 8.6 times the vortex separation, producing broad regular loops rather than fine ripples - Growth is fastest in a plane i...

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